Mechanical computer



Oct. 31, 1950 Filed June 4, 1949 W. H. NEWELL IECHANICAL COIPUTER 5Sheets-Sheet 1 Zhwentor Mum/v A! A swc'u Oct. 31, 1950 w, NEwELL2,528,284

MECHANICAL COMPUTER Filed June 4, 1949 5 Sheets-Sheet 2 ATTORNEY Oct.31, 1950 w. H. NEWELL MECHANICAL COIPUTER 5 Sheets-Sheet 3 Filed June 4.1949 Gttorneg 5 Sheets-Shea: 4

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- 3noentor fI VILL/A/V #514454 v e m 0 Mn a Oct. 31, 1950 w. H. NEWELLMECHANICAL COMPUTER 5 Sheets-Sheet 5 Filed June 4, 1949 Snventor bV/LL Mh. NEH/5L1.

(Ittomeg Patented Oct. 31, 1950 MECHANICAL COMPUTER William H. Newell,New York, N. Y., assignor to The Sperry Corporation, Long Island City,N. Y., a corporation of Delaware Application June 4, 1949, Serial No.97,159

12 Claims.

This invention relates to mechanical computers for solving problemsinvolving trigonometric functions and more particularly to a computerfor solving problems of the type arising in the control of gunfire.

An object is to provide a relatively simple and accurate device of theabove type.

Another object is to provide a device of the above type which may beused to obtain a plurality of computed quantities simultaneously.

Another object is to provide a device of the above type which is adaptedto the rapid and continuous solution of problems involving highermathematics.

Various other objects and advantages will be apparent as the nature ofthe invention is more fully disclosed.

The features of the invention will be better understood from thefollowing description, taken in connection with the accompanyingdrawings in which certain specific embodiments have been set forth forpurposes of illustration.

In the drawings:

Fig. 1 is a side elevation of a computer embodying the invention showingthe converting unit in sectiontaken along the line of Fig. 2.

Fig. 2 is a side elevation taken at right angles to the view of Fig. 1showing the converting unit in section taken along the line 22 of Fig.1.

Fig. 3 is a diagrammatic view illustrating the manner of operation ofthe device of Figs. 1 and 2.

Fig. 3a is a diagrammatic view taken on the line 3a-3a and in directionof the arrows in Fig. 3.

Fig. 4 is a schematic diagram illustrating a computer utilizing a pairof converting units.

Figs. 5, 6 and 7 are diagrammatic views illustrating the manner ofoperation of the device of Fig. 4.

Referring to Figs. 1 and 2 the converting unit comprises a fixed housingIll in which a rotatable housing H is mounted for rotation about avertical axis by ball bearings |2 held by a retaining ring It. Therotatable housing includes a gear 9 and a boss I! in which a sleeve i isfixed.

A shaft I5 is iournalled in ball bearings i1 and I8 carried by thesleeve I5 and carries at its top end a bevel gear I9 meshing with abevel gear 2|) which is freely mounted on ball bearings 2| for rotationabout a vertical shaft 22. The shaft 22 is journalled in ball bearings25 in a central boss 26 of the rotatable housing A spur gear 21 ispinned to the bevel gear 20.

The shaft It carries at its lower end a bevel gear 28 meshing with abevel gear 28 mounted on a hub 30 of a roller 3| which is rotatablymounted to rotate about a shaft 32 on ball bearings 33. The shaft 32 isfixed in an enlarged portion 34 of the sleeve |5.

A cylindrical cage 38 is mounted on ball bearings 39 and 40 to rotateabout the sleeve I5. The cage 38 carries a gear 4| meshingwith a gear 42fixed to the shaft 22. A gear 43 is also fixed at the top of the shaft22. The cage 38 carries a plurality of brackets 45 in which rollers 46are J'ournalled for rotation about axes lying in a plane perpendicularto the axis of the shaft I6. A ball 5|) contacts the rollers 45 and theroller 3|.

The ball 50 rides on the surface of another ball 5| which is restrainedfrom linear displacement by suitable bearings not shown. The arrangementis such that the axes of the shafts l5 and 22 intersect at the center ofthe ball 50, and the point of contact of the balls 50 and 5| lies in theaxis of the vertical shaft 22.

A pair of guide roller and 56 contact the surface of the ball 5| atpoints displaced by 90 around the ball 5| from each other and also fromthe point of contact of the ball 50.

The guide rollers 55 and 56 are mounted for rotation about shafts 51 and58 carried in yokes 59 and 60 which are pivoted on pins 6| and 62,respectively, whose axes lie in radii of the ball 5|. Arms 63 and 64 areattached to the pins 6| and 62 and are provided with forked ends 65 and66 having slots 61 and 68 engaging pins 69 and 10 mounted on racks IIand 12 which mesh with gears 12 and 14, respectively. The gears andracks are supported by means not shown.

The operation of a cage and ball provided with a guiding roller isdescribed in detail in my United States Patent No. 2,412,468, datedDecember 10, 1946, together with a mathematical analysis of the factorsinvolved. The present invention is a further development of that systemutilizing a second ball with two guiding rollers for shifting the axisof rotation of the balls as a function of the input quantities.

Referring to the diagram in Fig. 3 the ball 50 is in contact with theball 5| at the point V. The roller 55 is in contact with the ball 5| atthe point K and its axis is displaced from the vertical in the plane ofthe diagram (Figs. 1 and 3) by the angle A. The roller 58 is in contactwith the ball 5| at the point H and its axis is displaced fromthevertical in the plane of Fig. 3a by the angle D. When the angles Aand D are both zero, both balls 50 and 5| and the roller 3 rotat in theplane of the diagram (Fig. 3) and the cage 38 remains stationary.

The angles A and D are two angles whose tangents represent inputquantities introduced through gears 13 and 14 (Figs. 1 and 2). A thirdinput quantity may be the angular velocity V: of the roller 3| which isdriven by the gear 21 (Fig. 1). Vr may be constant to represent time ormay be variable. The output quantity may be represented by the rotationof the cage 30 about its axis as taken from the gear 03. The rotation ofthe cage 38 may, however, constitute an input quantity and the rate V:may constitute an output quantity.

In Fig. 3 the paths of the rollers 55 and 56 on the surface of the ball5| are indicated by circles 80 and 8| and the axis of rotation of theball 5| due to the positions of the guiding rollers 55 and 56 isindicated as O'O. The resultant path of the point V on the ball BI isrepresented by the circle 82.

In ball 50 the axis of rotation due to the guiding effect of the ball 5|and the roller 3| is indicated by 0-0 and the path of the point V on theball 50 is represented by circle 83.

A mathematical explanation of the relationship of th quantities follows:

In Fig. 3, in the right spherical triangle HKF, it is evident that theside KF is equal to the angle D.

In the right spherical triangle KFO the angle OKF the angle A, and sin Dtan A tan 1.

In the right spherical triangle VFO', the side FV=90-D, and tan 1 sec Dtan B.

On the ball 50, triangles VZO and V'ZO are similar, and

Sin a cot B=tan b=cot W Combining,

Cot W= sin a cot A cot D Where:

B is the angle between the plane determined by the axis O'O' of rotationof the ball 5| and the axis Y, and that determined by the point ofcontact K and the axis Y.

W is the angle between the axis 0-0 of the ball 50 and the plane Q ofthe cage rollers 40.

a is the angle between the axes of the ball 00 passing through thepoints of contact Z with the driving roller 3| and the point of contactV with the ball 5|.

2; is the angular displacement of the axis OO of the ball 50 in theplane d from the point of contact Z with the driving roller 3|. B=90W.

c is the angular displacement of the axis O0 of the ball 50 in the planeS from the axis of the ball 50 passing through the point of contact Vwith the ball 5|.

And, where:

Va is the angular velocity of the ball 00,

V:- is the angular velocity of the roller 3|,

k is the diameter of the driving roller 3| divided by the diameter ofthe ball 60, and

Vc is the angular velocity of the cage 30,

Ve sin b=kVr or Ve=kVr sin b V=V cos b Vc=kVr cos b/sin b Vc=ICVr/ tan bSince Cot W=sin a cot A cot D, and b=90-W tan b=sin a cot A cot DVc=kVr/S1n a cot A cot D,

4 or since sine a is constant for any particular construction,

Vc=k'Vr tan A tan D Hence if V: is introduced at the gear'fl, tan A atthe gear I3 and tan D at the gear I4, the rotation of the gear 43represents the output V: in the above equation. Of course Vc mayconstitute an input and V: an output. Other factors can be introduced byshifting the rollers 00 and 56 from the points indicated.

Fig. 4 shows a device including a pair of converting units in contactwith a common ball 00 at 180 points V and V. Since the units are bothsimilar to the unit of Figs. 1 and 2 all of the mechanical details havenot been repeated. The parts of one unit are designated by referencecharacters used for corresponding parts of Figs. 1 and 2 and the partsof the other unit are given the same reference characters with a primeadded.

In Fig. 4 the gears 43 and 40' drive pinions 00 and 90' which areconnected by shafts 0| and 0| and bevel gears 02 and 02' to oppositesides of a differential 03 having a spider connected to drive an outputshaft N.

The gears 21 and 21' drive pinions I00 and I00 which are connectedthrough shafts I 0| and IN and bevel gears I02 and I02 to opposite sidesof a differential I03 having a spider driving an output shaft Ill.

The ball i guided by a pair of drive rollers I 05 and I05 which in theembodiment shown make contact with the ball 05 at points K and H (Fig.5) which are located 90 apart and 90 from the points V and V. Therollers I00 and I06 are assumed to rotate about fixed axes normal to theradii of the ball 05 and lying in the same diametrical plane of theball. The axes of the rollers I05 and I00, however, could be orientedand the points of contact K, H, V and V could be shifted on the ball 05for introducing additional quantities.

Orientation of the axis of rotation of the ball 95 is determined by therelative surface velocities at the contact points H and K.

The axis M'M assumed by the ball 00 makes the angle F (Fig. 6) with theaxis of the ball through the point K. The angle F is equal to tan- Y/X,where Y and X are equal or proportional to the surface velocities at thepoints of contact K and H, respectively.

A third factor may be introduced by rotating the converter units by thegears I and 0' and pinions I01 and I01 through equal angles D (Fig. 6)and in opposite directions about the axis passing through the points ofcontact V and V.

The angle B is equal to angle F-I-angle D and the angle B is equal toangle F-angle D.

The surface velocity Av along path I00 at the points of contact V and Vis X sec F.

The component Gv of the surface velocity Av along the line G (Fig. 6) isAv cos B, and the component G'v along the line G is Av cos B. Zv is thesurface velocity of the point of contact Z of the roller 3| and the ball00, and Z'v is the velocity of the Point of contact Z of the roller IIand the ball 50'.

The components of the surface velocity Av along lines U and Uperpendicular to the lines G and G are Uv equal to Av sin B, and U'vequal to Av sin B, respectively. Referring now to the cage rollers 40and 40', Uv and U'v must be multiplied by the cosecant of the angle a(Pig.

Go=Au cos B=Av cos (F+D)= Av cos (tan- Y/X+D) Av=X sec F. Go=X sec F cos(tan- Y/X+D) G X(cos tan Y/X cos D-sin tan- Y/X sin D) Cos tan- Y/XGv=X(cos D-Y/X sin D) =X cos D-Y sin D Similarly G'o=Av cos B'=Av cos(F-D)= X cos D+Y sin D Uv=Ao sin B Aa Sill (F+D)= Y cos D+X sin DSimilarly,

U'o=Y cos D-X sin D L (the angular velocity of the cage 38) kUn=k (Y cosD+ sin D) L (the angular velocity of the cage 38)= kU'=k (Y cos DX sinD) Hence by introducing rates X and Y through rollers I06 and H15,respectively, and the angle D by gears 9 and 9' outputs Gt and Gv' areob tained from gears 21 and 21', outputs L and L' are obtained from cagegears 43 and 43'.

By adding the outputs Gv and G'v and Uv and Uv by means of thedifferentials I03 and 93, respectively, X cos D and Y cos D may beobtained on output shafts I and ill, respectively. Similarly bysubtracting the outputs Gv and Gv' and Uv and Uv', Y cos D and x sin Dmay be obtained.

Of course the various inputs and outputs may be interchanged accordingto the result desired. In some instances three or more converting unitsmay be used for obtaining still further quantities. One or both of therollers Hi5 and I06 may be replaced by converting units. In each ofthese instances different mathematical equations may be solved.

The units may be connected to a disc instead of the large ball 5| or maybe used to drive or be driven by a plane surface.

Other embodiments will be apparent to a person skilled in the art.

What is claimed is:

l. A computer comprising a rotatable ball restrained against lateralmovement, a pair of guide rollers contacting the surface of said ball atspaced points, and a converting unit comprising a second ball contactingthe surface of said first ball at a point spaced from said first points,a third roller contacting the surface of said second ball and in drivingrelationship therewith, a cage rotatable about an axis passing throughthe center of said second ball and inclined with respect to an axispassing through the centers of said balls, said cage carrying aplurality of cage rollers contacting said second ball in a diametricalplane thereof which is normal to the axis of said cage, each cage rollerrotating about an axis lying in said diametrical plane, a housingcarrying said cage and rotatable about the axis passing through thecenters of. said balls, means directing said housing about its axis,means in driving relationship to said third roller, means in drivingrelationship with said cage, means introducing quantities to be computedto certain of said driving means and means deriving computed quantitiesfrom other of said means.

2. In a computer as set forth in claim 1 means orienting the axes ofsaid first rollers in accordance with input quantities for altering theaxis of rotation of said first ball.

3. A computer as set forth in claim 1 in which said first rollers andsaid second ball contact said first ball at points 90 apart on thesurface of said first ball.

4. A computer as set forth in claim 1, means driving said third roller,orienting said housing about its axis and orienting the axes of saidfirst rollers in accordance with input quantities and means deriving anoutput quantity from said cage.

5. In a computer as set forth in claim 1 a second converting unitidentical with the first converting unit and having a ball contactingsaid first ball at a point 180 from the point of contact of said secondball, means orienting the housings of said units by equal amounts inopposite directions in accordance with an input quantity, means drivingsaid guide rollers in accordance with input quantities, means includinga differential connected to combine the outputs from the third rollersof the two units and means including a differential connected to combinethe outputs from the cages of the two units.

6. A computer comprising a rotatable member and a converting unitcomprising a ball contacting the surface of said member, driving meanscontacting the surface of said ball and in driving relationshiptherewith, a second driving means rotating about an axis at an angle tothe axis of the first driving means and in driving relationship withsaid ball, and means introducing quantities to be computed to saiddriving means.

'7. A computer comprising a rotatable member and a converting unitcomprising a ball contacting the surface of said member, a drivingroller contacting the surface of said ball and in driving relationshiptherewith, a cage rotatable about an axis passing through the center ofsaid ball and the point of contact of said driving roller and said balland having means to drive said ball, and means introducing quantities tobe converted to said driving roller and said cage.

8. A computer comprising a rotatable member and a converting unitcomprising a ball contacting the surface of said member, a drivingroller contacting the surface of said ball and in driving relationshiptherewith, a cage rotatable about an axis passing through the center ofsaid ball and the point of contact of said ball and said roller,

said cage carrying a plurality of cage rollers contacting said ball in adiametrical plane thereof which is normal to the axis of said cage, eachcage roller rotating about an axis lying in said diametrical plane, andmeans introducing quantitles to be computed to said first roller andsaid cage.

9. A computer comprising a rotatable ball restrained against lateralmovement and a converting unit comprising a second ball contacting thesurface of said first ball, driving means contacting the surface of saidsecond ball and in driving relationship therewith, a second drivingmeans rotating about an axis at an angle to the axis of the firstdriving means and in driving relationship to the said second ball, andmeans introdueing quantities to be converted to said driving means.

10. A computer comprising a rotatable member and a converting unitcomprising a ball contacting the surface of said member, driving meanscontacting the surface of said ball and in driving relationshitherewith, a second driving means rotating about an axis at an angle tothe axis of the first driving means and in driving relationship withsaid ball, a third driving means adapted to rotate the axis of one ofsaid driving means about the axis of the other of said driving means,and means introducing quantities to be computed to said driving means.

11. A driving means consisting of a converting unit comprising a ballcontacting a surface relative to which motion takes place, a drivingroller contacting the surface of said ball and in driving relationshiptherewith, a cage rotatable about an axis passing through the center ofsaid ball and the point of contact of said driving roller and said balland having means to drive said ball, and means for introducing orremoving quantities representing relative motion between the drivingmeans and surface through either or both the said driving roller andsaid cage.

12. The combination of a driving-means as set forth in claim 11 withmeans for rotating the converting unit about an axis passing through thecenter of said ball and the point of contact of the ball with thesurface, said means permitting changing the direction in which relativemotion is introduced or removed between the driving means and thesurface.

WILLIAM H. NEWELL.

No references cited.

